Question
Find the polynomial having roots at $ -1 $ , $ -7 $ , $ 1 $ , $ -9 $ , $ 2 $ and $ 0 $ .
Answer
The polynomial generated from the given zeros is: $ P(x) = x^6+14x^5+30x^4-140x^3-31x^2+126x $
Explanation
Step 1: Turn the zeros into factors:
| Zero | Factor |
| $ -1 $ | $ x+1 $ |
| $ -7 $ | $ x+7 $ |
| $ 1 $ | $ x-1 $ |
| $ -9 $ | $ x+9 $ |
| $ 2 $ | $ x-2 $ |
| $ 0 $ | $ x $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+1 \right) \cdot \left( x+7 \right) \cdot \left( x-1 \right) \cdot \left( x+9 \right) \cdot \left( x-2 \right) \cdot x = x^6+14x^5+30x^4-140x^3-31x^2+126x $$This page was created using
Polynomial From Roots Calculator